Patients with schizophrenia exhibit impaired neuronal network dynamics that can be targeted by non- invasive brain stimulation. In particular, rhythmic stimulation waveforms (transcranial alternating current stimulation, tACS) that enhance cortical synchronization may represent a targeted and therefore more effective approach to treat these network abnormalities. The long-term goal is to develop a new, noninvasive treatment for schizophrenia that is based on a mechanistic understanding of the network- level pathology. The overall objective of the R21 phase is to compare tACS and sham, with tDCS as a positive control for assay sensitivity, for treatment of auditory hallucinations in patients with schizophrenia in a double-blind, placebo-controlled pilot clinical trial. Additionally, the mechanism of action will be studied with electroencephalogram (EEG)-based biomarkers to elucidate the network- level effects of non-invasive brain stimulation. The objective of the R33 phase is to perform a double- blind, sham-controller clinical trial to assess the reduction in AHRS scores by five days of twice-daily tACS compared to sham stimulation (primary outcome) and the additional benefit of low-dose maintenance tACS (secondary outcome). The central hypothesis is that tACS is an effective treatment modality for auditory hallucinations and that the effectiveness of tACS correlates with changes in neuronal synchronization measured by EEG. The hypothesis will be objectively tested by pursuing the following specific aims: (R21: 1) evaluate tACS for the treatment of medication resistant auditory hallucinations in patients with schizophrenia, (R21: 2) elucidate the network-level mechanisms that are targeted by tACS and determine the predictive value of EEG synchronization measures for treatment outcome, and (R33: 3) perform a larger pilot clinical trial to assess tACS versus sham stimulation (primary outcome) and low-dose tACS maintenance treatment versus sham maintenance (secondary) outcome for reduction in AHRS scores. The significance of the proposed research is the chance of significant improvement in quality of life of affected patients with successfully treated medication resistant symptoms of schizophrenia, specifically auditory hallucinations.